JournalscmhVol. 75, No. 2pp. 232–246

The decomposition of 3-dimensional Poincaré complexes

  • J. Crisp

    Université de Bourgogne, Dijon, France
The decomposition of 3-dimensional Poincaré complexes cover
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Abstract

We show that if the fundamental group of an orientable PD3-complex has infinitely many ends then it is either a proper free product or virtually free of finite rank. It follows that every PD3-complex is finitely covered by one which is homotopy equivalent to a connected sum of aspherical PD3-complexes and copies of S1×S2S^1 \times S^2 . Furthermore, it is shown that any torsion element of the fundamental group of an orientable PD3-complex has finite centraliser.

Cite this article

J. Crisp, The decomposition of 3-dimensional Poincaré complexes. Comment. Math. Helv. 75 (2000), no. 2, pp. 232–246

DOI 10.1007/PL00000372